Introduction strong coupling: polaritons sample

1. PROBING THE BOGOLIUBOV EXCITATION SPECTRUM OF A POLARITON SUPERFLUID BY HETERODYNE FOUR-WAVE-MIXING SPECTROSCOPY Verena Kohnle, Yoan Leger, Maxime Richard, Michiel Wouters, Marcia Portella-Oberli, Benoit Deveaud-Pledran

2. Outline • Introduction • strong coupling: polaritons • sample • Motivation: excitation spectrum of a polariton superfluid • Heterodyne Four Wave Mixing (FWM) experiment • Experimental Results • Conclusion

3. Strong coupling regime: Polaritons Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Picture: Kasprzak et al. Nature (2006) Polaritons are composed bosons: Photonic content: provides high degree of coherence Excitonic content: interaction between polaritons Polariton: quasi particle composed by a photon coupled to an exciton Microcavity 2D system for photons; Quantum well  2D system for excitons Polaritons are the new eigenstates of the system in the strong coupling regime

4. Sample • AlAs/GaAs– cavity which contains a 8 nm In0.04Ga0.96As quantum well (QW) • Bragg mirrors: contain 26.5 and 20 pairs of alternated /4 layers of AlGaAs and AlAs • wedged cavity spacer layer •  the resonator frequency of • the resonator can be • varied by moving the laser • spot over the sample • rabi splitting: 3.4 meV top DBR ••• Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook 8nm QW In0.04Ga0.96As λ-cavity Substrate (GaAs) ••• bottom DBR space

5. Polariton superfluid: Bogoliubov dispersion Polaritons : weakly interacting bose gas Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook • feature of interactions: •  blueshift of dispersion •  BOGOLIUBOV Dispersion: • linear at small k • „ghost“ branch In experiment: up to now nobody was able to show the „ghost“ branch

6. State of the art No Bogoliubov ghostbranchobserved: A proposal as an answer: Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Wouters et al. PhysRev B,79, 125311 (2009) Utsunomiya et al. Nature, 4, 700 (2008) Wouters et al. PhysRev B,79, 125311 (2009)

7. our method: • using heterodyne Four-Wave-Mixing (FWM) setup • fs-laser  broad energy spectrum (~12meV) •  normal and gohst branch are • probed with the same laser pulse Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook 10 I0 FWM I0 energy -k0 0 +k0 wavevector k

8. Heterodyne FWM setup Miror Pinhole Lens Ref (0,0) Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook balanced detection Pump (0,w1) Sample FWM (-k,2w1-w2) Trigger (k,w2) Heterodyne Channels: A (j=0) B (j=p) to CCD AOM @ 2w1-w2 • best sensitivity • spectral interferometry • amplitude & phase resolution • balanceddetection • background suppression

9. Bogoliubov: tracking the ghost branch Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook normal branch ghost branch k=0 k = 1 µm-1

10. Dispersion of the Bogoliubov excitations evolution in k of the different branches: (delay integration between 5 – 6 ps) Gross-Pitaevskii equations: Equation for excitons: Equation for cavity photons: Yx/p= exciton/photon wavefunction g = exciton-exciton interaction potential gx/p= decay rate of excitons/photons 2WR= Rabi splitting F(r,t)= pump laser field Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook

11. Bogoliubov: excitation power dependence evolution in excitation power: (@ delay time t=5.7ps) Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook k = 1 µm-1 Arb. Int. = 16

12. Bogoliubov: excitation power dependence evolution in excitation power: (@ delay time t=5.7ps) 2 ng Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook ng k = 1 µm-1 Arb. Int. = 16

13. Bogoliubov: excitation power dependence evolution in excitation power: (@ delay time t=5.7ps) Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook k = 1 µm-1 Arb. Int. = 16

14. conclusion & outlook • Observation of the Bogoliubov excitation • spectrum of a polariton superfluid using • heterodyne FWM spectroscopy • we demonstrate unambigously the excistence • of the negative energy „ghost“ branch • Outlook: 2D FT allows to characterice th apperence of the • different resonances Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook THANK YOU !